Löwner equations and dispersionless hierarchies

Details Löwner equations and dispersionless hierarchies Löwner equations and dispersionless hierarchies

2006-05-06

arxiv.org/abs/math/0605161v1

Mathematics

Complex Variables

30 pages, 5 figures, amsart.cls, graphics.sty, psfrag.sty etc. are used

Scientific paper

10.1088/0305-4470/39/37/010

Using the Hirota representation of dispersionless dKP and dToda hierarchies, we show that the chordal L\"owner equations and radial L\"owner equations respectively serve as consistency conditions for one variable reductions of these integrable hierarchies. We also clarify the geometric meaning of this result by relating it to the eigenvalue distribution of normal random matrices in the large N limit.

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